I am handling refinement data for which crystal structure is reported in C 1 2/c 1 space group. I want to know what is the difference between C 1 2/c 1 and C 2/c (with unique axis 'c') space groups. It will be also helpful if one can comment on how to transform the co-ordinates of former phase in to c 2/c settings. waiting for your kind comment or note on it.. Thank you in advance....
The WYCKPOS tool at the Bilbao Crystallographic Server (http://www.cryst.ehu.es) is useful for this. It lists the spacegroup in both settings, and by comparison it is obvious how the coordinates are related.
C 2/c with unique axis b is the setup, in which the symmetry elements conform to the name: The C-side of the unit cell is centered, the 2-fold axis is parallel b, and the c glide plane normal to b generates a shift along c.
In C 2/c with unique axis c the symmetry elements are like this: The A-side of the unit cell is centered, the 2-fold axis is parallel c, and the c glide plane normal to c generates a shift along a. Accordingly the proper name of the space group in this setup would be A 2/a.
A third setup, B 2/b, can be constructed accordingly.
Also it should be noted that each of these setups has two different possibilities for the preferred axis. E.g. C 2/c can have unique axis b, in which case the full Hermann–Mauguin notation is C 1 2/c 1, but could also have unique axis a, which would be C 2/c 1 1. Only by giving the full Hermann–Mauguin notation, uncertainties can be avoided in this space group.
Another option is PowderCell. It does it automatically if you insert the structure as *.cel-file. You can select then any setting and you will get the lattice as well as the atomic positions automatically transformed. The test is the powder diffraction pattern which will be calculated for both settings and should not show any difference.
Attached is a pdf-file which you have to rename into PowderCell.zip and then unpack it somewhere. There is no installation required. Although quite old it works even with Windows10.
Dear Prof. Nolze and Prof. Tobbens,
Thank you for sharing your valuable time and knowledge to clear my querries regarding the unit cell transformation. I had tried unit cell transformation with powder cell and is working well. But still I have one query in my mind, is there any atom which should be present at (0,0,0.5) position to satisfy 'c' centering. instead I have (1/4, 1/4, 0.5) co-ordinates for one of the 4d (wyckoff) site. I mean that the C centering is not essentially face centering. (Please correct me if I may not be correct). Thank you once again.
The centering describes the position of the lattice point but no atomic position! The lattice point represents the entire motif of the structure. The motif itself reflects the space group symmetry. The asymmetric unit commonly used for a crystal structure description is only a part of the motif, i.e. applying the symmetry operators on the asymmetric unit the motif results. The third button from left in PowderCell displays a structure info which lists all atomic position of the unit cell, i.e. also positions of lattice centerings, but again: only very rare monoclinic structures have an atom position with the coordinates 0,0,0, and only then you would get then an additional position 0.5, 0.5, 0 in your list of atomic positions (using the info in PowderCell).
As already commented other times I am against using computing programs as black boxes; a crystallographer must know basic crystallography and not just push buttons. The question posed by Banghe D.S. is a typical basis transformation which can be managed by transformation matrices. If we call M the matrix transforming a base a, b, c, in a new base a’, b’, c’, the atom coordinates x’, y’, z’ in the new base are obtained from the original ones by the inverse (M-1) of the transpose matrix (MT), i.e. (MT)-1. The same matrices can be used to transform the reciprocal basis and the indices hkl.
Besides, as already noted by Daniel M. Többens, if the basis is changed, normally also some symbols may change. In the present case the space group C12/c1 (unique axis b) becomes B112/b if the original b and c axes are exchanged. If, instead, are the original a and c axes to be exchanged the symbol of the space group becomes A112/a.
A suggested textbook for basic an general crystallography is C. Giacovazzo (editor) “Fundamentals of Crystallography”, Oxford 2011.
Dear Giovanni, you are certainly right, but who is nowadays still "crystallographer"? More and more material scientists are dealing with crystal data and don't get the fundamentals in a sufficient way so that I am not surprised about such a question. We need to enforce the education of crystallographers (again since obviously the general meaning is that crystallography is a science which is not developing anymore and therefore more and more universities close crystallographic institutes), and simultaneously need to offer tools for non-crystallographesr that they don't need to read entire books to change a setting. Nevertheless, regarding crystallographers you are certainly right. But also for crystallographers I would bet an optimistic wager that only 50% can do this (despite the fact that is quite easy).
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